Vehicle stability control system and method

ABSTRACT

A method and system for controlling vehicle stability may comprise determining whether a vehicle is oversteering or understeering and, if the vehicle is oversteering or understeering, determining an amount by which to reduce a speed of the vehicle to correct for understeering or oversteering and applying brake pressure to at least the rear brakes of the vehicle to reduce vehicle speed. The method and system also may comprise determining an engine torque reduction amount based on vehicle oversteer or understeer conditions, reducing engine torque by the determined amount or to zero if the determined amount of engine torque reduction is greater than an actual engine torque, and applying braking to at least the rear brakes of the vehicle if the determined amount of engine torque reduction is greater than the actual engine torque.

FIELD

The present invention relates generally to a motor vehicle stabilitycontrol system that regulates the longitudinal tire forces of a vehicleto improve the vehicle's lateral stability indirectly.

INTRODUCTION

The primary objectives of electronic stability control (ESC) systems areto prevent vehicles from spinning (oversteer) or plowing out(understeer). Prevention of oversteer and understeer is generallyachieved by controlling the vehicle in response to both yaw rate andsideslip angle, which are values indicative of lateral motion of avehicle. Using a vehicle's steering wheel angle as a gauge of thedriver's desired yaw rate, the system determines the difference betweendesired yaw rate and actual yaw rate, and can take measures to help thedriver stay on course. On low friction surfaces, however, controllingonly a vehicle's yaw rate may not be sufficient to prevent the vehicle'ssideslip angle from building up. Large sideslip angles are generallyundesirable because they cause reduced maneuverability orcontrollability of the vehicle. For stability in all driving conditions,sideslip angle (and its derivative(s)) can be used by the system as anadditional feedback signal.

Electronic stability control systems normally rely on the application ofbrake pressure for control authority. Application of brake pressure atan appropriate corner of the vehicle can generate a yaw torque todirectly correct understeering or oversteering of the vehicle.Therefore, electronic stability control can also be referred to asdirect yaw control. In some instances, the applied corrective yaw torquemay not be enough to keep the vehicle on the road, for example when thespeed of the vehicle is too great for available traction. In such acase, it may be desirable to slow the vehicle by reducing engine torqueand/or applying four-wheel braking. At a reduced speed, a cornering tireforce required to balance the centrifugal force can be reduced to thepoint where the vehicle can negotiate a curve and the average driverwill be able to regain control of the vehicle, without being reduced ata rate or to a degree that itself causes any loss of control. Thus,vehicle lateral stability can be indirectly improved by controllinglongitudinal tire forces. Longitudinal tire forces are the forcesgenerated by the tire parallel to the direction the tire is rolling(front to back). Longitudinal tire forces can be manipulated directlywith the vehicle brakes and the powertrain.

SUMMARY

The present invention may address one or more of the above-mentionedissues. Other features and/or advantages may become apparent from thedescription which follows.

Various exemplary embodiments of the invention provide a method andsystem for controlling vehicle stability. The method and system maycomprise determining whether a vehicle is oversteering or understeeringand, if the vehicle is oversteering or understeering, determining anamount by which to reduce a speed of the vehicle to correct forundersteering or oversteering and applying brake pressure to at leastthe rear brakes of the vehicle to reduce vehicle speed.

Various exemplary embodiments of the invention alternatively oradditionally provide a method and system that comprise determining andrive axle torque amount based on vehicle understeer or oversteerconditions, reducing engine torque by the determined amount or to zeroif the determined axle torque is less than zero, and applying braking toat least the rear brakes of the vehicle if the determined axle torque isless than zero.

In the following description, certain aspects and embodiments willbecome evident. It should be understood that the invention, in itsbroadest sense, could be practiced without having one or more featuresof these aspects and embodiments. It should be understood that theseaspects and embodiments are merely exemplary and explanatory and are notrestrictive of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Features and advantages of the claimed subject matter will be apparentfrom the following detailed description of embodiments consistenttherewith, which description should be considered with reference to theaccompanying drawings, wherein:

FIG. 1 is a flow diagram illustrating an exemplary embodiment of avehicle stability control system and method according to the presentteachings;

FIG. 2 is a linear two-degree-of-freedom bicycle model;

FIG. 3 schematically illustrates distribution and realization oflongitudinal tire force by regulating brake pressure at each wheel inaccordance with various exemplary embodiments of the present teachings;

FIG. 4 illustrates an exemplary embodiment of an engine torque requestthat includes a negative engine torque request;

FIG. 5 illustrates how an engine torque reduction module and a curvaturecontrol module can work together in accordance with various exemplaryembodiments of the present teachings;

FIG. 6 is a flow diagram for a curvature control module in accordancewith various exemplary embodiments of the present teachings; and

FIG. 7 illustrates a friction circle.

Although the following detailed description makes reference toillustrative embodiments, many alternatives, modifications, andvariations thereof will be apparent to those skilled in the art.Accordingly, it is intended that the claimed subject matter be viewedbroadly.

DETAILED DESCRIPTION OF VARIOUS EMBODIMENTS

Reference will now be made to various embodiments, examples of which areillustrated in the accompanying drawings. However, these variousexemplary embodiments are not intended to limit the disclosure. To thecontrary, the disclosure is intended to cover alternatives,modifications, and equivalents.

FIG. 1 is a flow diagram illustrating the teachings of an embodiment ofa vehicle stability control system and method of the present invention.As shown, from sensor signals such as, for example, steering wheel angleand vehicle speed, as well as a vehicle model, a target lateral response(or driver intent) is derived and an actual lateral response is eitherdirectly measured (e.g., via yaw rate (YR)) or estimated (e.g., viasideslip gradient (SSG) and sideslip angle (SSA)) for example via acontroller. A controller of the present invention can include one ormore controllers and can be integrated into an existing vehicle rollstability controller or yaw stability controller or can be a dedicatedcontroller receiving one or more inputs from the roll stabilitycontroller and/or the yaw rate controller. The controller can evaluatevehicle speed and road condition, as well as the actual and the targetlateral responses. The controller can also compare target and actuallateral responses and, if the controller determines that the vehiclemotion deviates too much from the driver intent, it can apply brakepressure at the outside corners (oversteer situations) or inside corners(understeer situations) of the vehicle to reduce the deviation.Depending on how effectively vehicle motion is corrected (i.e., howeffectively the deviation is reduced), the controller can then determinewhether it is necessary to further slow the vehicle by reducing enginetorque and/or applying two- or four-wheel braking. From a driver's pointof view, engine torque reduction can be preferable to braking, becauseit generally feels less intrusive.

To reduce engine torque, various exemplary embodiments of the presentteachings can utilize an engine torque reduction (ETR) module thatlimits or reduces the driver's throttle input to decrease vehicle speed,which can improve the vehicle's lateral stability. The engine torquereduction module can use as its control signal the difference betweenthe measured yaw rate and the target yaw rate (or the difference betweenthe target and actual lateral response measurements). The driver'sdesired yaw rate can be estimated using a linear two-degree-of-freedombicycle model based on steering wheel angle and speed (see FIG. 2). Thistarget represents idealized vehicle behavior on high p. High p is a highroad surface friction corresponding, for example, to dry asphalt.

From this control signal, the engine torque reduction module candetermine a torque command that can be realized by the vehicle'spowertrain and perhaps its brake systems. It can help a driver maintaincontrol of a vehicle when the vehicle has entered a curve at too high aspeed. It can also be used to prevent a driver from accelerating to aspeed that is too high for a particular curve.

An engine torque reduction module reduces engine torque to slow avehicle, causing a decrease in the vehicle's turning radius. Ifnecessary, the engine torque reduction module can send a decelerativetorque request to a curvature control module that uses braking to slowthe vehicle additionally and/or more quickly.

In some exemplary embodiments, the engine torque reduction module isintended to control longer term understeer and oversteer and remaininactive or limited during transient conditions. In such embodiments, acheck for quasi steady-state cornering can be utilized. The direction ofthe target yaw rate (or target lateral response), the measured yaw rate(or actual lateral response), and the lateral acceleration can bealigned when the vehicle is not transitioning from one direction toanother. If this steady-state cornering check is not met, controldeadbands of the engine torque reduction module can be increased, asdescribed below, desensitizing the engine torque reduction module'scontrol during transient maneuvers. Control deadbands are control signalranges where no action occurs in the engine torque reduction module.

To limit the engine torque reduction module's vehicle control toappropriate situations and leave throttle control to the driver innormal driving circumstances, certain embodiments of the presentinvention can use dynamic control activation deadbands that increase anddecrease in size. In various exemplary embodiments, these deadbands canbe the sum of three components, a yaw rate controller deadband, asteady-state cornering component, and a transition component that can bebased on sideslip angle. The yaw rate controller deadband can beincluded so that the engine torque reduction module activates after theyaw controller, which is designed to control yaw rate over relativelyshort time periods compared to the engine torque reduction module. Thedeadbands take the following form:

DB _(ETR) =DB _(yawcontrol) +DB _(steadystate)+max (0, k_(sideslip)*(μ*CC _(rear)±Sideslip_(linear)))   (1)

where μ is the estimate of the coefficient of friction in g, CC_(rear)is the cornering compliance of the rear axle in deg/g, k_(sideslip) is again that determines the magnitude of the contribution of the transitioncomponent based on the sideslip angle, and Sideslip_(linear) is a linearestimate of the sideslip at the rear axle in degrees. Sideslip_(linear)can be calculated outside of the curvature control and engine torquereduction modules. It is calculated using a linear bicycle model withconstant cornering compliances and assuming a high μ. Corneringcompliance is a measure of how much slip angle at the front or rear axlewill build with lateral acceleration in (slip angle (indegrees))/(lateral acceleration (in g's)). Sideslip_(linear) can besubtracted from the other terms for left turns and added for rightturns, assuming ISO sign convention. This transition component is largerwhen the side slip estimate is small and smaller when the side slipestimate is large. The transition component desensitizes the enginetorque reduction module's control during transitional maneuvers. Thetransition component of the deadband desensitizes the controller duringtransitions because Sideslip_(linear) becomes small or zero during thetransition. This leaves μ*CC_(rear), which is a positive constant, asthe dominant term. During steady state, Sideslip_(linear) is equal to orclose to μ*CC_(rear) and they cancel each other out or almost canceleach other out, which makes the deadband term smaller and the controllermore sensitive. During transition, when Sideslip_(linear) does notcancel μ*CC_(rear), the deadband component is at a maximum and thecontroller is desensitized. In addition to the transition component,DB_(steadystate) increases to a larger value when the steady statecornering check is not met and decreases to a smaller value when thesteady state cornering check is met. Both DB_(yawcontrol) andDB_(steadystate) have different ranges depending on whether the vehicleis understeering or oversteering.

The control signal for the engine torque reduction module can becalculated for all four cases of turning left or right with understeeror oversteer. For example, turning left, understeer:

YawSignal_(ETR)={dot over (ψ)}_(tgt)−{dot over (ψ)}_(measured) −DB_(ETR,L,US)   (2)

Turning right, understeer:

YawSignal_(ETR)={dot over (ψ)}_(measured)−{dot over (ψ)}_(tgt) −DB_(ETR,R,US)   (3)

Turning left, oversteer:

YawSignal_(ETR)−{dot over (ψ)}_(measured)−{dot over (ψ)}_(tgt) −DB_(ETR,L,OS)   (4)

Turning right, oversteer:

YawSignal_(ETR)={dot over (ψ)}_(tgt)−{dot over (ψ)}_(measured) −DB_(ETR,R,OS)   (5)

The largest of these four values is used as the engine torque reductionmodule control signal. The engine torque reduction module control signalis then multiplied by −1 so that positive values increase the enginetorque request and show that the yaw rate error is smaller in magnitudethan the deadband. Negative values of the engine torque reduction modulecontrol signal signify that engine torque should be decreased andindicate that the yaw rate error is greater than the deadband.

YawSignal_(ETR)=−1*YawSignal_(ETR)   (6)

The controller can perform PID control (proportional, integral,derivative control for automatically adjusting variables to hold a valueconstant) of the axle torque based on the control signal (see equation6) using the equations:

$\begin{matrix}{T_{proportional} = {k_{p}*{YawSignal}_{ETR}}} & (7) \\{T_{derivative} = {k_{d}*\frac{{YawSignal}_{ETR}}{t}}} & (8) \\{T_{integral} = {k_{i}*{\int{{YawSignal}_{ETR}*{t}}}}} & (9)\end{matrix}$

The requested axle torque from engine torque reduction module can thenbe defined as:

T _(ETR) =T _(derivative) +T _(proportional) +T _(int egral)   (10)

In addition, T_(ETR) can be filtered and its rate of change can belimited so that control actuation is smooth and progressive. IfT_(ETR)<0, the engine will not be able to realize the torque request. Inthis case, the torque request can be sent to a curvature control modulewhere the brakes can be applied to generate the necessary deceleration,as described below.

In accordance with various exemplary embodiments of the presentteachings, the control logic can require that three conditions are metto activate the engine torque reduction module:

YawSignal_(ETR)<0   (11)

T_(ETR)<T_(Driver)   (12)

T_(ETR)<T_(TCS)   (13)

where T_(Driver) is the driver axle torque request estimated fromthrottle and engine speed, and T_(TCS) is the TCS axle torque request.If the engine torque reduction module is already active, the firstcondition (shown in equation 11) may not be used. In such a case, theengine torque reduction module request will be increasing toward thedriver and traction control system (TCS) requests. The engine torquereduction module can remain active until its request has matched thelower of the driver and TCS requests, maintaining a smooth transitionout of the engine torque reduction module's control. When the enginetorque reduction module is not active, T_(int egral) is set accordingto:

T _(int egral)=min(T _(Driver) ,T _(TCS))−T _(derivative) −T_(proportional)   (14)

This initializes the integral component of PID control so that the totaltorque request of the engine torque reduction module can be held at thesmaller of the driver and TCS torque requests until activation occurs.Upon activation, the engine torque reduction module torque request canfollow PID control to ensure that the torque request is continuous whentransitioning from inactive to active control states.

However, the most an engine torque reduction module can typically do istake away a driver's throttle input and let the vehicle slow itself viainertia (coast). In cases where a controller determines that a vehicleshould be slowed more quickly or to a greater extent, a curvaturecontrol module can be employed to activate and apply brake pressure totwo or four wheels. A curvature control module can be employed inaddition to an engine torque reduction module or as an alternative to anengine torque reduction module. Further, the curvature control modulecan be a part of the engine torque reduction module, or can be anindependent module. The curvature control module can run on the samecontroller as the engine torque reduction module, or can run on its owncontroller or a controller shared with other modules for vehiclecontrol. Compared with engine torque reduction, which can reduce thedriving force, curvature control can impose a negative longitudinalforce (or drag force) on the vehicle.

In an exemplary embodiment of the present teachings, in a case where theconditions of vehicle oversteer or understeer are so great that thecurvature control module should be utilized, the curvature controlmodule receives an (unrealizable) negative engine torque request (seeFIG. 4), for example from the engine torque reduction module. A negativeengine torque request results from the controller determining thatvehicle speed should be reduced by an amount or rate greater than can beachieved by reduction of throttle input—e.g., the controller hasdetermined that the engine not only needs to stop adding to vehiclespeed, but also needs to apply a certain amount of drag on the vehicle(and the engine generally cannot be used to apply a sufficient drag onthe vehicle). The curvature control module can translate the negativeengine torque request into a longitudinal force, as described in moredetail below. The longitudinal force can then be distributed andrealized by regulating brake pressure at each wheel, as illustrated inFIG. 3. Thus, a negative engine torque request is input to the curvaturecontrol module, which converts that request into braking commands foreach wheel on the vehicle.

According to some exemplary embodiments, in a steady-state corneringevent, curvature control does not make the vehicle oversteer orundersteer, and can allow the vehicle to remain within a predeterminedpercentage of its maximum cornering capacity to maintain a properbalance between short-term and long-term path curvature optimizationtrade-offs. The curvature control algorithm can employ an automaticbraking algorithm that prevents oversteering and understeering, allowsthe vehicle to remain within a predetermined percentage of its maximumcornering capacity, and can be effective in reducing turning radius byregulating brake pressure at each wheel.

For sustained driver over-command of steering wheel angle (e.g.,understeer, where the driver is commanding more yaw rate with thesteering wheel than the vehicle can deliver, including events beyond atransient event such as a two-lane change or making a right or leftturn), the vehicle's electronic stability control may determine that thevehicle cannot achieve the driver desired path for the given vehiclespeed and road conditions. In some cases, any resulting appliedcorrective direct yaw torque cannot significantly increase the netcornering power or ability of the vehicle to match the driver's desiredyaw rate without forcing the vehicle into a buildup of sideslip angle.Therefore, the engine torque reduction module reduces engine torque toslow the vehicle to allow a decrease in turning radius. However, enginetorque reduction may not be able to reduce vehicle speed quickly enough,since engine response can be relatively slow, and in general cannot beused to impose a drag force on the vehicle. Further, engine torquereduction only works when the driver is on throttle; since otherwise,there is no throttle input to deduct from. Nevertheless, the enginetorque reduction module may determine that it is necessary to furtherslow the vehicle via a negative torque/force (see FIG. 4), whichgenerally cannot be realized by the vehicle's engine. Althoughdownshifting can perhaps add some drag, often, particularly with anautomatic transmission, more drag may be desired than the transmissioncan achieve.

In accordance with some exemplary embodiments of the present teachings,curvature control and engine torque reduction modules can work together,as illustrated in the schematic diagram of FIG. 5, to slow the vehicle.If the engine torque reduction module requests a positive drive torquevalue that is smaller than a driver throttle value or engine tractioncontrol request value (in a vehicle where traction control is occurringsimultaneously and its value is compared with the engine torquereduction module request and whichever is smaller is used), the enginetorque is reduced, but not completely taken away (i.e., it is reduced tothe requested positive drive torque value). On the other hand, if therequested drive torque value is negative, it is determined that not onlyshould the engine torque be eliminated, but also a negative longitudinalforce should be applied. The curvature control module is then utilizedto translate the “desired” negative engine torque command (or negativelongitudinal force) into brake actuator or brake pressure commands.

As illustrated in FIG. 5, in various exemplary embodiments, the enginetorque reduction module can receive feedback in the form of actual yawrate, which can be used to control torque reduction. Similarly, thecurvature control module can receive feedback in the form of actualengine torque, which can be used to control braking.

FIG. 6 illustrates a main flow diagram for the curvature control modulein accordance with certain embodiments of the invention. At block 4,inputs are received from various sensors and calculations frompreviously-executed code (e.g., sideslip angle (as calculated, forexample, by an external module), normal load (as calculated, forexample, by an external module), and a request from the engine torquereduction module (T_(ETR)). Other inputs could include, for example,brake pressure estimates (for each wheel), brake master cylinderpressure, indication of driving direction (forward or backward),longitudinal velocity, indication of the driver applying the brakes, alinear calculation of the front axle slip angle, tire normal load (foreach wheel), tire steer angle (or its sine and cosine), a rear sideslipangle estimate. At block 6, the curvature control module determines acontrol flag and a curvature control torque, as described in more detailbelow. At block 8, front tire force is calculated or estimated, and issubsequently used to estimate the road friction coefficient μ in block10. At block 12, the normalized longitudinal force NX_(steer) induced bythe driver's steering input is determined, and is used in calculatingthe requested longitudinal force NX_(request) at block 14. Exit andenter conditions are calculated at block 16, e.g., longitudinal speedbeing>5 m/s, a counter limiting how long curvature control can activatefor, and side slip angle being less than a predetermined angle. Thecounter can be used to make a smooth transition between application ofcurvature control and removal of curvature control. A control command (aunitless measure NX between 1 and 0 of how much the vehicle should slowdown, which is used to determine pressure values) is determined at block18 and converted into brake actuator commands (or brake pressurerequests) at block 20.

If the engine torque command (T_(ETR)) from the engine torque reductionmodule is negative, a curvature control torque (T_(CC)) is calculated,and a flag (CC_(torque)) is set to indicate that the curvature controlis required:

T _(CC)=min(T _(ETR), 0)   (15)

CC _(torque)=(T _(CC)<0)   (16)

The rest of the algorithm translates T_(CC) into a normalized negativelongitudinal force, which is then redistributed to the four corners ofthe vehicle in proportion to the normal load on that corner.

The front tire lateral force in vehicle plane (F_(Tf)) is estimatedbased on lateral acceleration (a_(y)) and the derivative of yaw rate({dot over (r)}):

$\begin{matrix}{F_{Yf} = {{M \cdot a_{y} \cdot \frac{b}{a + b}} + {\frac{I_{z}}{a + b} \cdot \overset{.}{r}}}} & (17)\end{matrix}$

where M is the mass of the vehicle, a is the distance from vehiclecenter of gravity to front axle, b is the distance from vehicle centerof gravity to rear axle, and I_(z) is the moment of inertia about theyaw axis. F_(Yf) is then converted to the lateral force in tire plane(see FIG. 7):

$\begin{matrix}{F_{yf} = \frac{F_{Yf} - {{F_{xf} \cdot \sin}\; \delta}}{\cos \; \delta}} & (18) \\{F_{yfl} = {F_{Yf} \cdot \frac{\eta_{fl}}{\eta_{fl} + \eta_{fr}}}} & (19) \\{F_{yfr} = {F_{yf} - F_{yfl}}} & (20)\end{matrix}$

in which δ is the front wheel steer angle, and η_(fl) and η_(7 fr)represent the normalized normal load on front left and front rightwheel, respectively. The front longitudinal forces (F_(xf)) in the tireplane can be calculated using the estimated caliper pressure (P_(fl)_(—) _(est), P_(fr) _(—) _(est)):

F _(xfl)=−ρ_(F) _(—) _(Bar2N) ·P _(fl) _(—) _(est)   (21)

F _(xfr)=−ρ_(F) _(—) _(Bar2N) ·P _(fr) _(—) _(est)   (22)

F _(xf) =F _(xfl) +F _(xfr)   (23)

where ρ_(F) _(—) _(Bar2N) is a conversion factor from front brakepressure to longitudinal force, and is a constant with units N/bar.

A rough measure of the road surface friction coefficient (μ) is based onthe front tire force information and the lateral acceleration, forexample:

$\begin{matrix}{\hat{\mu} = {\max\left( {\frac{a_{y}}{g},\frac{\sqrt{F_{xf}^{2} + F_{yf}^{2}}}{\left( {\eta_{fl} + \eta_{fr}} \right) \cdot M \cdot g}} \right)}} & (24)\end{matrix}$

where g is acceleration due to gravity. The computed value {circumflexover (μ)} is further limited to a minimum value of approximately 0.1,and to a maximum value of 1.0. Once {circumflex over (μ)} is determined,the maximum tire force—the product of normal force and {circumflex over(μ)}—can be determined for the given driving condition. The normalizedtire force can also be determined, for example as the ratio of tireforce and maximum tire force. For example, the normalized front brakingforce is calculated as follows:

$\begin{matrix}{{NX}_{brake} = \frac{{- 2} \cdot P_{MC} \cdot \rho_{F\_ {Bar}2N}}{\left( {\eta_{fl} + \eta_{fr}} \right) \cdot \hat{\mu} \cdot M \cdot g}} & (25)\end{matrix}$

where P_(MC) is a master cylinder pressure measurement. Similarly, thenormalized front longitudinal force requested by the driver is given by

$\begin{matrix}{{NX}_{driver} = \frac{{{{- 2} \cdot P_{MC} \cdot \rho_{{F\_ {Bar}2}\; N} \cdot \cos}\; \delta} - {{F_{y}}\sin \; \delta}}{\left( {\eta_{fl} + \eta_{fr}} \right) \cdot \hat{\mu} \cdot M \cdot g}} & (26)\end{matrix}$

The difference between NX_(driver) and NX_(brake) represents thelongitudinal force due to driver steering. That is

NX _(steer) =NX _(driver) −NX _(brake)   (27)

Note that the calculations of NX_(driver), NX_(brake) and NX_(steer) canbe saturated such that they all belong to [−1, 0].

Due to NX_(steer), one can imagine that the front tires already workharder than the rear tires to reduce vehicle speed. This situation isillustrated in FIG. 3, far left, as the vehicle heads forward in thedirection indicated by arrow V_(x). The tire force vectors areillustrated by arrows for each tire. In order to add a balance to thevehicle during the process of slowing it down, some exemplaryembodiments of the curvature controller can start with increasing brakepressure only on the rear wheels to swing the rear tire force vectorbackwards (see central illustration of FIG. 3) until it is in parallelwith the front tire force vector. Then, if needed, both the front andrear tire pressure are increased simultaneously (see far rightillustration of FIG. 3), so that the front and rear tire force vectorsare kept in parallel and are further rotated backwards. The magnitude ofthe individual tire forces are designed to be in proportion to thenormal force on that wheel.

To have the same effect as NX_(steer), the rear wheel brake pressuresare given by

$\begin{matrix}{P_{{rl}\_ {steer}} = {- \frac{{NX}_{steer} \cdot \eta_{rl} \cdot \hat{\mu} \cdot M \cdot g}{\rho_{{R\_ {Bar}2}\; N}}}} & (28) \\{P_{{rr}\_ {steer}} = {- \frac{{NX}_{steer} \cdot \eta_{rr} \cdot \hat{\mu} \cdot M \cdot g}{\rho_{{R\_ {Bar}2}\; N}}}} & (29)\end{matrix}$

where ρ_(R) _(—) _(Bar2N) is a conversion factor from rear brakepressure to longitudinal force, and η_(rl) and η_(rr) represent thenormalized normal load on rear left and rear right wheel, respectively.If the sum of P_(rl) _(—) _(steer and P) _(rr) _(—) _(steer) and isequivalent to a higher longitudinal force than T_(CC) is, T_(CC) cansimply be translated into the brake pressure of the rear wheels. T_(CC)is then reset to zero. Otherwise, T_(CC) can be adjusted to take intoaccount the steering effect. See the following logic:

${if}\mspace{14mu} \left( {\frac{- T_{CC}}{R_{tire} \cdot \rho_{R\_ Bar2N}} < {P_{rl\_ steer} + P_{rr\_ steer}}} \right)${$P_{rl\_ steer} = {\frac{- T_{CC}}{R_{tire} \cdot \rho_{R\_ Bar2N}}\frac{\eta_{rl}}{\eta_{rl} + \eta_{rr}}}$$P_{rl\_ steer} = {\frac{- T_{CC}}{R_{tire} \cdot \rho_{R\_ Bar2N}} - P_{rl\_ steer}}$T_(CC) = 0 } else T_(CC) = T_(CC) + (P_(rl)_steer + P_(rr)_steer) ·ρ_(B)_Bar2N · R_(tire)where R_(tire) is the tire rolling radius.

The adjusted T_(CC) can then be converted to a normalized longitudinalforce

$\begin{matrix}{{NX}_{CC} = \frac{T_{CC}}{R_{tire} \cdot \hat{\mu} \cdot M \cdot g}} & (30)\end{matrix}$

Note that NX_(CC)≦0, since T_(CC)≦0. A normalized longitudinal curvaturecontrol request can be determined as

NX _(request) =NX _(steer) +NX _(CC)   (31)

Furthermore, in certain embodiments of the invention, NX_(request) canbe limited such that it does not exceed NX_(min), which is a designparameter normally chosen as −0.6 (i.e., 60% of the total tire force):

if (NX _(request) <NX _(min))

NX_(request)=NX_(min)

The limit helps prevent brake pressure from getting so high that lateraltire force is washed out, which means that brake pressure gets so highthat it generates a longitudinal tire force that reduces the tire'slateral force capability.

Another consideration for limiting NX_(request) is preventing rapidbrake pressure buildup from increasing path radius by imposing a

$\frac{R}{t} \leq 0$

condition in certain embodiments of the invention, where R is pathradius. If NX is the requested normalized longitudinal force of theprevious control loop, and assuming that tire force has reached itslimit, it follows from Newton's Second Law that:

$\begin{matrix}{R = \frac{v^{2}}{\sqrt{1 - {NX}^{2}} \cdot g \cdot \hat{\mu}}} & (32)\end{matrix}$

in which v is the vehicle speed. From equation (32), the derivative of Rwith respect to time is calculated:

$\begin{matrix}{\frac{R}{t} = {{{\frac{2 \cdot v}{\sqrt{1 - {NX}^{2}} \cdot g \cdot \hat{\mu}} \cdot \frac{v}{t}} + {\frac{\left( {1 - {NX}^{2}} \right)^{- 1} \cdot v^{2} \cdot {NX}}{\sqrt{1 - {NX}^{2}} \cdot g \cdot \hat{\mu}} \cdot \frac{{NX}}{t}}} \leq 0}} & (33)\end{matrix}$

which can be further simplified as

$\begin{matrix}{{{2 \cdot \frac{v}{t}} + {\left( {1 - {NX}^{2}} \right)^{- 1} \cdot v \cdot {NX} \cdot \frac{{NX}}{t}}} \leq 0} & (34)\end{matrix}$

Note that the deceleration of the vehicle dv/dt is given by

$\begin{matrix}{\frac{v}{t}{{NX} \cdot g \cdot \hat{\mu}}} & (35)\end{matrix}$

Substituting (35) into (34) results in the following lower bound on thechanges in NX_(request):

dNX _(min)=−2·Δt·g{circumflex over (μ)}·(1−NX ²)/v   (36)

if (NX _(request) <NX+dNX _(min))

NX _(request) =NX+dNX _(min)

where Δt is a sampling period (or control loop time). Similarly, toprevent sudden decrease in radius, a

$\frac{R}{t} \geq 0$

condition can be imposed so that the pressure request does not drop toofast. Following the same steps as in (32)-(36), an upper bound on thechanges in NX_(request) can be obtained:

dNX _(max)=2·Δt·g·{circumflex over (μ)}·(1−NX ²)/v   (37)

if (NX _(request) >NX+dNX _(max))

NX _(request) =NX+dNX _(max)

In some exemplary embodiments, to ensure that curvature controlfunctions only when it is needed, a counter CC_(counter) can be designedaccording to the following logic:

if ( (CC_(torque) || ((NX_(request) ≦ NX_(steer) ) && CC_(enable) )) &&(| {circumflex over (β)} |< β_(Limit) ) ) {   if (CC_(counter) <MAX_(loop))    CC_(counter) = CC_(counter) + 1 } else if (CC_(counter) >0)   CC_(counter) = CC_(counter) − 1where MAX_(loop) is a design parameter, {circumflex over (β)} is theestimated sideslip angle and β_(Lim) is its limit, and CC_(enable) isthe previous loop enter/exit flag. The curvature controller can beenabled when the counter does not indicate “Time Out” and the vehiclespeed is greater than 5 (m/s). That is,

CC _(enable)=(v>5 m/s)&&(CC _(counter)>0)   (38)

The curvature control command NX for this loop can thus be determined asfollows:

if (CC _(enable))NX=NX _(request)

else NX=NX_(steer)

NX can then be translated into individual brake pressure request inproportion to the normal load on that wheel:

if (CC_(enable)) {$P_{fl\_ cc} = {{- \frac{1}{\rho_{F{\_ Bar2N}}}}\left( \left. {{{NX} \cdot \eta_{fl} \cdot \hat{\mu} \cdot M \cdot g} +} \middle| {{F_{yfl} \cdot \sin}\mspace{14mu} \delta} \right| \right)\frac{1}{\cos \; \delta}}$(39) if (P_(fl)_cc > CC_(counter) · Δt · MAX_(rate)) P_(fl)_cc =CC_(counter) · Δt · MAX_(rate)$P_{fr\_ cc} = {{- \frac{1}{\rho_{F{\_ Bar2N}}}}\left( \left. {{{NX} \cdot \eta_{fr} \cdot \hat{\mu} \cdot M \cdot g} +} \middle| {{F_{yfr} \cdot \sin}\mspace{14mu} \delta} \right| \right)\frac{1}{\cos \; \delta}}$(40) if (P_(fr)_cc > CC_(counter) · Δt · MAX_(rate)) P_(fr)_cc =CC_(counter) · Δt · MAX_(rate)$P_{r{l\_ cc}} = {P_{rl\_ steer} - {\frac{1}{\rho_{R{\_ Bar2N}}}{\left( {{NX} - {NX}_{steer}} \right) \cdot \eta_{rl} \cdot \hat{\mu} \cdot M \cdot g}}}$(41) if (P_(rl)_cc > CC_(counter) · Δt · MAX_(rate)) P_(rl)_cc =CC_(counter) · Δt · MAX_(rate)$P_{{rr}{\_ cc}} = {P_{rr\_ steer} - {\frac{1}{\rho_{R{\_ Bar2N}}}{\left( {{NX} - {NX}_{steer}} \right) \cdot \eta_{rr} \cdot \hat{\mu} \cdot M \cdot g}}}$(42) if (P_(rr)_cc = CC_(counter) · Δt · MAX_(rate)) P_(rr)_cc =CC_(counter) · Δt · MAX_(rate) else { P_(fl)_cc = 0 P_(fr)_cc = 0P_(rl)_cc = 0 P_(rr)_cc = 0 }where MAX_(rate) is a design parameter that limit how fast the pressurerequests can change per loop.

Utilizing the above curvature control module, alone or in addition to anengine torque reduction module, vehicle stability control can beimproved.

For the purposes of this specification and appended claims, unlessotherwise indicated, all numbers expressing quantities, percentages orproportions, and other numerical values used in the specification andclaims, are to be understood as being modified in all instances by theterm “about.” Accordingly, unless indicated to the contrary, thenumerical parameters set forth in the written description and claims areapproximations that may vary depending upon the desired propertiessought to be obtained by the present invention. At the very least, andnot as an attempt to limit the application of the doctrine ofequivalents to the scope of the claims, each numerical parameter shouldat least be construed in light of the number of reported significantdigits and by applying ordinary rounding techniques.

Notwithstanding that the numerical ranges and parameters setting forththe broad scope of the invention are approximations, the numericalvalues set forth in the specific examples are reported as precisely aspossible. Any numerical value, however, inherently contains certainerrors necessarily resulting from the standard deviation found in theirrespective testing measurements. Moreover, all ranges disclosed hereinare to be understood to encompass any and all subranges subsumedtherein. For example, a range of “less than 10” includes any and allsubranges between (and including) the minimum value of zero and themaximum value of 10, that is, any and all subranges having a minimumvalue of equal to or greater than zero and a maximum value of equal toor less than 10, e.g., 1 to 5.

It is noted that, as used in this specification and the appended claims,the singular forms “a,” “an,” and “the,” include plural referents unlessexpressly and unequivocally limited to one referent. Thus, for example,reference to “a restraint device” includes two or more differentrestraint devices. As used herein, the term “include” and itsgrammatical variants are intended to be non-limiting, such thatrecitation of items in a list is not to the exclusion of other likeitems that can be substituted or added to the listed items.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the systems and methods ofthe present disclosure without departing from the scope its teachings.Other embodiments of the disclosure will be apparent to those skilled inthe art from consideration of the specification and practice of theteachings disclosed herein. It is intended that the specification andexamples be considered as exemplary only.

1-12. (canceled)
 13. A system for controlling vehicle stability, thesystem comprising: a controller for receiving one or more of inputsignals from vehicle sensors and calculations from previously-executedcode, and, if the vehicle is oversteering or understeering, reducing aspeed of the vehicle to correct for understeering or oversteering,wherein the controller sends a signal to apply brake pressure to variousbrakes of the vehicle to reduce vehicle speed, until an actual vehicleresponse close enough to a target vehicle response, and wherein thetarget vehicle response is based on at least a steering wheel angle anda vehicle speed, and the actual vehicle response is based on a vehicleyaw rate or a vehicle sideslip gradient and sideslip angle.
 14. Thesystem of claim 13 wherein, upon initially applying brake pressure torear wheels of the vehicle, balance is added to the vehicle whileslowing the vehicle by swinging a rear tire force vector backwards untilit is in parallel with a front tire force vector.
 15. The system ofclaim 14, wherein brake pressure is applied to front and rear brakes ofthe vehicle simultaneously after application of brake pressure to therear brakes of the vehicle.
 16. The system of claim 15 wherein, if brakepressure is applied to the front and rear brakes of the vehiclesimultaneously, the brake pressure is applied so that the front and reartire force vectors are kept in parallel and are further rotatedbackwards.
 17. The system of claim 16, wherein the magnitude of thebrake pressure applied to each brake is in proportion to the normalforce on the wheel to which the brake pressure is applied.
 18. Thesystem of claim 13, wherein the controller determines oversteer andundersteer by comparing a target vehicle yaw rate with an actual vehicleyaw rate.
 19. The system of claim 13, wherein the controllerdesensitizes control during transient maneuvers using control deadbands.20. A system for controlling stability of a vehicle, the systemcomprising: a brake system; and a controller configured to control thebrake system and receiving one or more of input signals from vehiclesensors and calculations from previously-executed code indicative ofwhether a vehicle is oversteering or understeering and, if the vehicleis oversteering or understeering, reducing a speed of the vehicle tocorrect for understeering or oversteering, wherein the controller sendsa signal to apply brake pressure to a wheel at an outside corner if thevehicle is oversteering, sends a signal to apply brake pressure to awheel at an inside corner if the vehicle is understeering, and sends asignal to apply brake pressure to the vehicle's rear wheels ifapplication of brake pressure at the outside corner wheel or insidecorner wheel does not make an actual vehicle response close enough to atarget vehicle response, and wherein the target vehicle response isbased on at least a steering wheel angle and a vehicle speed, and theactual vehicle response is based on a vehicle yaw rate or a vehiclesideslip gradient and sideslip angle.
 21. The system of claim 20wherein, upon initially applying brake pressure to the rear wheels ofthe vehicle, balance is added to the vehicle while slowing the vehicleby swinging a rear tire force vector backwards until it is in parallelwith a front tire force vector.
 22. The system of claim 21, whereinbrake pressure is applied to front and rear brakes of the vehiclesimultaneously after application of brake pressure to the rear brakes ofthe vehicle.
 23. The system of claim 22 wherein, if brake pressure isapplied to the front and rear brakes of the vehicle simultaneously, thebrake pressure is applied so that the front and rear tire force vectorsare kept in parallel and are further rotated backwards.
 24. The systemof claim 23, wherein the magnitude of the brake pressure applied to eachbrake is in proportion to the normal force on the wheel to which thebrake pressure is applied.
 25. A system for controlling stability of avehicle, the system comprising: a brake system; and a controller forreceiving one or more of input signals from vehicle sensors andcalculations from previously-executed code indicative of whether avehicle is oversteering or understeering and, if the vehicle isoversteering or understeering, reducing a speed of the vehicle tocorrect for understeering or oversteering, wherein the controller sendsa signal to apply brake pressure to a wheel at an outside corner if thevehicle is oversteering, sends a signal to apply brake pressure to awheel at an inside corner if the vehicle is understeering, and sends asignal to reduce engine torque if application of brake pressure at theoutside corner wheel or inside corner wheel does not make an actualvehicle response close enough to a target vehicle response, and whereinthe target vehicle response is based on at least a steering wheel angleand a vehicle speed, and the actual vehicle response is based on avehicle yaw rate or a vehicle sideslip gradient and sideslip angle. 26.The system of claim 25, wherein brake pressure is applied to rear wheelsof the vehicle if application of brake pressure at the outside cornerwheel or inside corner wheel does not make the actual vehicle responseclose enough to the target vehicle response.
 27. The system of claim 26wherein, upon initially applying brake pressure to rear wheels of thevehicle, balance is added to the vehicle while slowing the vehicle byswinging a rear tire force vector backwards until it is in parallel witha front tire force vector.
 28. The system of claim 27, wherein brakepressure is applied to front and rear brakes of the vehiclesimultaneously after application of brake pressure to the rear brakes ofthe vehicle.
 29. The system of claim 28 wherein, if brake pressure isapplied to the front and rear brakes of the vehicle simultaneously, thebrake pressure is applied so that the front and rear tire force vectorsare kept in parallel and are further rotated backwards.
 30. The systemof claim 29, wherein the magnitude of the brake pressure applied to eachbrake is in proportion to the normal force on the wheel to which thebrake pressure is applied.